Answer to Question #278849 in Physics for Simmy

Question

A door with width 1.2 m and mass M mass 10kg is hinged on one side so that it can rotate freely a bullet is fired into the center of the door the bullet has mass 25gand speed of 300ms what is angular velocity of the door with respect to the hinge just after the bullets embeds itself in the door

Answer 1

Angular momentum imparted by bullet on the door

$$L=mvr=(0.025)(300)(0.6)=4.5\frac{kgm}{s}$$

Moment of inertia of the door, 

$$I=\frac{1}{3}Ml^2=\frac{1}{3}(10)(1.2)^2=4.8\ kg m^2\\\omega=\frac{4.5}{4.8}=0.9375\frac{rad}{s}$$